A Boolean algebra algorithm suitable for use in …homepage.ntu.edu.tw/~cmliao/Data/pdf/2005/Computers... · 2013-06-29 · Computers and Electronics in Agriculture 48 (2005) 1–18

Computers and Electronics in Agriculture 48 (2005) 1–18

A Boolean algebra algorithm suitable for use intemperature–humidity control of a grafted

seedling acclimatization chamber

Li-John Joua,b, Chung-Min Liaob,∗, Yi-Chich Chiua

a Department of Biomechatronic Engineering, National Ilan University,Ilan, Taiwan 260, People’s Republic of China

b Ecotoxicological Modeling Center, Department of Bioenvironmental Systems Engineering,National Taiwan University, Taipei, Taiwan 10617, People’s Republic of China

Received 1 July 2004; received in revised form 18 November 2004; accepted 31 December 2004

Abstract

The objective of this paper was to link a psychometric chart and Boolean algebra algorithms ondeducing the procedural and logical issues of temperature–humidity environmental control for agrafted seedling acclimatization chamber. We developed a condition-sequence control circuit basedon Boolean algebra algorithms to solve the complex logical problem existing in temperature–humidityenvironmental control procedures. A Matlab program was used to deduce and simplify the Booleanrelations between input and output logical variables of the controller, whereas the correctness ofBoolean function was verified by an Excel program. The Boolean functions were firstly transformedto switching (logical) circuits and subsequently transformed to a programmable logical controller(PLC) program systematically. We implemented the developed industrial wiring devices and PLCin designing a temperature–humidity environmental controller of an acclimatization chamber forgrafted seedlings in that we adopted the nonlinear control technique associated with the condition-sequence control methodology as the main control scheme. On the other hand, we adopted thecompound control action, two-position set point action, the time-delay control and the conditionalaction of free cooling as the main control operations for the controller. Our results demonstratethat the overall seasonal survival rate was 97% by using the Boolean algebra-based controlled

∗ Corresponding author. Tel.: +886 2 2363 4512; fax: +886 2 2362 6433.E-mail address:[email protected] (C.-M. Liao).

0168-1699/$ – see front matter © 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.compag.2004.12.008

2 L.-J. Jou et al. / Computers and Electronics in Agriculture 48 (2005) 1–18

chamber grafting, which was higher than that of 90% by employing the field grafted seedlingoperations.© 2005 Elsevier B.V. All rights reserved.

Keywords: Acclimatization chamber; Condition-sequence control; Boolean algebra; Psychrometrics; Pro-grammable logical controller

1. Introduction

Grafting can strengthen not only the disease resistance ability, but also can promotethe production quality of vegetable/fruit crops. Grafted seedlings are extensively usedin Asian countries such as Korea, Japan and Taiwan, where cultivated land is poor andintensively used. The purpose of grafting has greatly expanded because it reduces theeffect of soil-borne infectious diseases, increases the ability to tolerate low-temperatureand salt and wet-soil, enhances water and nutrient uptake and increase plant vigor toextend the duration of economical harvest time (Chiu et al., 1999). Grafted seedlingsare popular in Taiwan for watermelon, bitter gourd, eggplant and cucumber, where wa-termelon is the majority with 30 million seedlings per year for about 20,000 ha of field(http://www.coa.gov.tw/statistic/newyearbook/PDF/).

Vegetable grafting joins the stock and scion together by a clipper and/or pipe. Sinceboth the stock and scion are cut for grafting, they need to reconstruct their bundles in theprocess of acclimatization. For watermelon grafting, the stock is cut about 12 and 18–20days after seeding in summer and winter, respectively. The scion merely needs 4 days togrow after seeding in summer and 7 days in winter. Generally, the seedlings take about 7–10days to coalesce under controlled environment (Chiu et al., 1999). Both the grafting andpost-grafting curing operations significantly affect the survival rate of grafted seedlings.Nobuoka et al. (1996)pointed out that higher relative humidity (RH) was advantageous tocoalesce and to prevent the grafted seedlings of tomatoes from wilting. An improper curingenvironment will cause the seedlings to languish, produce over-growth, or even die.

In the present status of post-grafting curing operations, the seedlings are moved to theunder protected cover in the field, where climate violently affects the curing environment.The farmers must regulate the indoor environment by venting, covering, shading, etc. whenthe weather changes.Chiu et al. (1999)suggested that the optimal air temperature, RH andlight and dark interval period were 25–28◦C, 90% and 12 h, respectively, for acclimatinggrafted seedlings of watermelon.Chang et al. (2003)suggested that the survival rate andquality of grafted seedlings were promoted if the RH in the acclimatization chamber wasmaintained at 80–90%, whereas under 70% RH both indexes were greatly decreased. Anaverage light intensity of 25–49�mol m−2 s−1 could promote the leaf area, and fresh and dryweight of grafted seedlings. The suitable nursing temperature would be at 26–29◦C, whereasat 32–35◦C, the leaf area, fresh and dry weight of grafted seedlings were significantlydecreased.

Most mathematical models for microclimate control were mainly built on the theoryof mass–energy equilibrium (Papadakis et al., 1994; Wang and Boulard, 2000; Young et

http://www.coa.gov.tw/statistic/newyearbook/pdf/

L.-J. Jou et al. / Computers and Electronics in Agriculture 48 (2005) 1–18 3

al., 2000; Trigui et al., 2001; Pasgianos et al., 2003). In nonlinear conditions, the climateparameters in mathematical models are calculated by numerical methodologies such asRunge–Kutta and Newton–Raphson methods, which are complicated computational proce-dures. Most mathematical models were not easily implemented to control on-line, and themajor difficulties were divergence problems caused by choosing wrong initial state-variablevectors.

Vassilyev (1997)suggested that it was better to consider the discrete time in logi-cal methods for analysis and modeling of the controlled systems.Bemporad and Morari(1999)proposed a framework for modeling and controlling systems to describe interde-pendent physical laws, logic rules, and operating constrains, denoting as mixed logicaldynamical (MLD) systems. MLD systems include linear hybrid systems, finite state ma-chines, some classes of discrete event systems, constrained linear systems and nonlin-ear systems which can be approximated by piecewise linear functions. Boolean algebraplays a major role in computer sciences and can be used to represent sets and formu-las of propositional logical and digital circuits (Buttner and Simonis, 1987). Boolean al-gebra algorithms are a conscientious deducing rule for deciding a logical control path.Rosen (1999)suggested that the Quien–McCluskey method could build optimal expres-sions by systematically grouping the together-products when the number of input logi-cal variables exceeds four. The algorithm was tedious to use by hand, yet was very suit-able to program for computer calculation (Ross and Wright, 1999). Thus, we adopted theQuien–McCluskey method as the main simplifying methodology for the present logicalnetworks.

The objective of this paper was to develop an environmental controller for providing asuitable curing environment in a grafted seedlings acclimatization chamber. Specifically,the main goals of this paper were 4-fold: (1) to construct a logical control mathematicalmethodology by applying Boolean algebra algorithms to solve the complex logical prob-lem existing in temperature–humidity environmental control procedures, (2) to deduce andsimplify the Boolean expressions between input and output variables for the logical systemby using the Matlab program, using an Excel program to verify the correctness of Booleanfunction, (3) to transform Boolean functions to switching (logical) circuits and then toprogressively transform to a PLC program and (4) to implement the Boolean algebra algo-rithm in designing a temperature–humidity environmental controller of an acclimatizationchamber for grafted seedlings in that the nonlinear control technique associated with thecondition-sequence control methodology was adopted as the main control scheme. Thecompound control actions, two-position set point action, the time-delay control and theconditional action of free cooling were adopted as the main control operations for thecontroller.

2. Materials and methods

2.1. Experiment

The dimensions of the acclimatization chamber were 540 cm× 265 cm× 210 cm with a5 cm thick insulation and 185 cm inner height (Fig. 1). The chamber accommodated nine


Fig. 1. (a) The seedlings were kept on the culture-carts in the chamber after grafting, (b) vegetable grafting is tojoin the stock and scion together by a clipper and/or pipe and (c) cross section of an acclimatization chamber forgrafted seedlings.


culture-carts. Each cart consisted of five layers with four trays in each layer. The chamberhad a capacity of 12,960 seedlings and 72-cell trays were used.Chiu et al. (1999)suggestedthat an air speed lower than 0.2 m s−1 could prevent the grafted seedlings from wilting andachieve the reconstruction of bundles. The uniform air circulation and distribution in thechamber was regulated by three rows of 10-cm fans with five fans for each row, and astainless steel net.

The chamber equipped with artificial daylight, free cooling, humidifier, heater and airconditioner was used to provide a suitable curing environment for seedling after grafting(Fig. 1c). A 40 W straight plant-lamp (FL-40SBR/38) was mounted on the top of eachlayer in the cart to maintain constant spatial illumination in the chamber. The plant-lampsin the chamber were controlled by a 24-h timer. The chamber can be regarded as a heat-isolated system from outside so that sunlight does not affect the inner environment. Theheat produced by plant-lamps was followed by the assigned temperature–humidity controlstrategies. Ventilation openings installed on both sides of the chamber were controlled bytimer to periodically accommodate CO2 concentration. If the outside temperature and RHwere suitable for curing of grafted seedlings, ambient air was introduced to regulate thechamber environment to save energy. The artificial daylight and CO2 concentration in thechamber were then regulated by the time-sequence control method. We used ultrasonichumidifiers with the total capacity of 9 L h−1 to humidify the incoming air to preventulceration of the coalescent part of the grafted seedlings from fog. A 2 KW heater was usedto warm or dehumidify indoor environment. An air conditioner (20.0 MJ h−1) was equippedto provide a cooler environment.

Chiu et al. (1999)pointed out that the spatial variation of temperature, RH and air speedin the chamber was insignificant in that variations for temperature, RH and air speed werearound 1◦C, 3.6% and <0.2 m s−1, respectively. As a result, the microclimate in the chambercan be treated as a completely mixed and uniform environment. The variation of temperatureand humidity then can be simplified to a function of only time. The temperature–humidityenvironment was modulated by a control method of a feedback conditions-sequence.

The acclimatization chamber was equipped with an environmental controller deployed bylinking Boolean functions and a psychrometric chart to regulate indoor environment. Timerscontrolled hourly air exchange to modulate CO2 concentration. We verified the functionsof the environmental controller seasonally. Temperature–humidity recorders (HOBO-H08-032-08, Onset Computer Corp., U.S.A.) were installed both inside and outside of the cham-ber for recording the temperature–humidity variations on a daily basis at a 1-min samplingrate.

We processed the acclimating experiments of the grafted seedlings to obtain the survivalrates for comparing the grafted seedlings kept in the chamber with that moved in the fieldunder protected cover during the acclimating stage in spring (autumn), summer and winter.Consequently, the survival rates of the grafted seedlings were qualified and quantified bymeasuring the physical survival indices of grafted seedlings including the length of stockand scion, the diameter of stock and scion, leaf area and chlorophyll as a consulting indexof evaluation. We observed the state of reconstructing bundles in the coalescent part byfluorescence in order to determine whether the grafted seedlings were sustained-healthilysurvived. Each obtained datum was 1000 replicate plants after 14 days of grafting in spring,summer and winter, respectively.


2.2. Control framework

Fig. 2a illustrates the control framework for the system. The target of temperature–humidity environmental field confined by a psychrometric chart was regarded as a finitearea bounded by lower and upper limits of temperature (TL −TH) and RH (RHL − RHH),respectively. According to the upper–lower state of temperature and RH sensors, thetemperature–humidity environment was mainly divided into nine parts (– ) in a psychro-metric chart (Fig. 2b and c). There were 162 states of temperature–humidity environmentassociated with the outside, inside and illuminative time conditions. When the initial orproceeding state was disturbed by external factors such as weather changes and workeractivities, and temperatures and RH fell outside the control target area, the control strate-gies were quickly actuated to achieve the control target by operating mechanical equip-ment. Free cooling was operated automatically to save energy while indoor and outdoortemperature–humidity were both in the control target. The control paths formulated byBoolean functions and psychrometric processes could systematically perform and achievethe control rules and target settings.

The inputs of temperature and RH sensor states for PLC were the discrete finite states.In most control circuits of complex electrical systems, it is frequently necessary to makeintricate interconnections of relay contacts and switches. We adopted Boolean algebra al-gorithms to deduce the switching function that completely expressed as whole control pro-cesses in any state. A temperature–humidity environmental controller in a grafted seedlingsacclimatization chamber was implemented by adding on-line control strategies of time-sequence. The combination control circuit for the system mainly consisted of forward(comparing and two-position control actions), core (logic- and time-sequence) and output-load circuits (Fig. 3).

2.3. Psychrometric processes

Fig. 2b shows a psychrometric chart of cooling, dehumidifying, heating and humidify-ing control processes in a grafted seedlings acclimatization chamber. The area confined bylines was a control target of temperature and humidity in a psychrometric chart, whereasthe area bounded by dotted lines was the control target of two-position setting. In sum-mer, the outdoor temperature was higher than that of indoor and the initial state of thetemperature–humidity environment in the chamber was assumed on the outside boundary( – ). The psychrometric processes formulated by the principles of air-conditioning andhumidifying are shown as paths 1–4 inFig. 2b.

Since the outdoor temperature is typically lower than that of indoors in winter, the indoorRH is usually higher than the upper-limit RH (RHH). For this condition, the heater is startedto reduce the indoor RH until the two-position setting of RH (RHH′ ) is reached. The controlprocess is shown as path 5 inFig. 2b. When the indoor temperature–humidity environmentis in the g- or h-state, the heater and humidifiers are operated by formulating the controlpaths to regulate the indoor temperature–humidity environment for achieving the target oftwo-position setting (paths 6–10 inFig. 2b).

Fig. 2c shows a psychrometric chart of natural heating, dehumidifying, humidifyingand free cooling control processes in an acclimatization chamber for grafted seedlings.

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Fig. 2. (a) The diagram of a control framework for the system in a grafted seedlings acclimatization chamber, (b) a psychrometric chart of cooling, dehumidifying,heating and humidifying control processes in a grafted seedlings acclimatization chamber and (c) a psychrometric chart of natural heating, dehumidifying, humidifyingand free cooling control processes in an acclimatization chamber for grafted seedlings.


Fig. 3. The combinative diagram of the temperature–humidity environmental controller for a grafted seedlingsacclimatization chamber.

In summer, when the heat sources in the chamber were produced by the plant-lamps, thepsychrometric processes expressed by the paths of natural heating, dehumidifying andhumidifying are as shown by paths 11–14 inFig. 2c. If the indoor temperature–humidityenvironment is in the f-state, the heat sources produced by the plant-lamps can be used to de-crease the indoor RH without operating the heater. The control process is shown as path 15 inFig. 2c. When the plant-lamps were switched on, whereas the indoor temperature–humidityenvironment was still kept at the f-state after exceeding 3 min. The heater could be startedto reduce the indoor RH automatically.


In spring, autumn, and summer nights, when the indoor temperature–humidity environ-ment was in the d- or e-state, the indoor temperature–humidity environment was periodicallyregulated by the free cooling. The plant-lamps were then switched on by a timer. If the RHin the chamber was reduced by the heat, resulting in a RH that was lower than the lower-limit RH (RHL), the humidifiers must be switched on until the RH reached the target oftwo-position setting (paths 16–18 inFig. 2c).

2.4. Mathematic model

A control circuit consisting of forward, core and output-load circuits was integratedto implement the system (Fig. 3). Both two-position setting and comparing circuits weremajor parts of the forward circuit. The comparing and two-position control action cir-cuits could be represented as a mathematical pattern of equivalence by the followingexpressions:

XL ={

1 X(t) ≤ w

0 X(t) > w, XL′ =

{1 X(t) ≥ z

0 X(t) < z,

RL(T + 1) = [XL + RL(T )] · X̄L′ , (1)

XH ={

1 X(t) ≥ u

0 X(t) < u, XH′ =

{1 X(t) ≤ v

0 X(t) > v,

RH(T + 1) = [XH + RH(T )] · X̄H′ , (2)

[w, z] and [v, u] ∈ R,

whereX(t) is a time-dependent state-variable produced by a sensor,XH andXH′ the uncom-plemented logical variables of the upper-limit contact commanded by comparing circuits,XL andXL′ the uncomplemented logical variables of the lower-limit contact commanded bycomparing circuits,̄XH′ andX̄L′ the complemented logical variables,RH(T) andRL(T) thelogical variables denoted by virtual relays at the present state (T), RH(T+ 1) andRL(T+ 1)the logical variables denoted by virtual relays at the next state (T+ 1) andw, z, v andu arethe setting values in registers and comparators.

The core circuit mainly consisted of logical and time-sequence circuits. They werealso expressed as a mathematical pattern of equivalence by the Boolean functions. Then input variables canonical form (the sum of products) of Boolean functions can beexpressed as:

Yk = fk(x1, x2, . . . xn) = (ck1x1 · x2 · x3 . . . xn−1·xn + ck2x1 · x2 · x3 . . . xn−1 · xn

+ ck3x1 · x2 · x3 . . . · xn−1 · xn + . . . ck2(n−1)x1 · x2 · x3 . . . xn−1 · xn

+ ck2nx1 · x2 · x3 . . . xn−1 · xn) =2n∑i=1

cki · mi−1, (3)


wherek is the number of output variables,x the uncomplemented logical variables,x thecomplemented logical variables,Cki the constant (1 or 0) andmi−1 is the numerical formexpressed by the product of logical variables.

We used a Boolean matrix form to express the Boolean functions (Edwards, 1972):

[C] · X] = F ], (4)

where [C] = [Cki]k×2n , X] = [x1, x2, . . ., xn]T, andF] = [ f1, f2, . . ., fk]T in that [C] is theconstant (0 or 1) matrix in that [C] is also the matrix established and transposed by the truthtable of output operations,X] the input logical variable vector andF] is the output logicalfunction vector.

In this paper, the number of input logical variablesX produced by a virtual relay is9 (n= 9) and the number of output logical functionf is 4 (k= 4). Logical issues linkedby a temperature–humidity environmental control procedure and a psychrometric chartassociated with a Boolean algebra algorithm were hidden in the truth table including 29 = 512states. We adopted a Boolean matrix form to systematically express the functions (thedetailed derivation may be requested from the authors). The constructed processes andresults are described in the subsequent sections.

2.5. Deducing Boolean functions and implementation

We treatedw andz as well asu andv (Eqs.(1) and(2)) representing the two-positionsetting value of the lower and upper limit of temperature and RH, respectively, in thatwe definedw = TL(RHL), z=TL′ (RHL′ ), u=TH(RHH) andv = TH′ (RHH′ ). In the forwardcircuits (Fig. 3), we defined the variablesXHit ,XLit ,XHih,XLih,XHot,XLot,XHoh,XLoh,XHit ,RLit , RHih, RLih, RHot, RLot, RHoh andRLoh corresponding to the denoting subscripts of H,L, i, o, t, h and′, respectively, representing the upper limit, the lower limit, indoor, outdoor,temperature, humidity and two-position setting, e.g.,

XHit ={

1 Xit (t) ≥ TH

0 Xit (t) < TH, XHit′ =

{1 Xit (t) ≤ TH′

0 Xit (t) > TH′,

RHit(T + 1) = [XHit + RHit(T )] · X̄Hit′ , (5)

XLit ={

1 Xit (t) ≤ TL

0 Xit (t) > TL, XLit ′ =

{1 Xit (t) ≤ TL′

0 Xit (t) > TL′,

RLit (T + 1) = [XLit + RLit (T )] · X̄Lit ′ (6)

The other expressions of forward circuits could also be obtained (Fig. 3). The inputand output variables (x1, x2, . . ., x9 andY1, . . ., Y4) for the core circuit were respectivelyexpressed as the following expressions:

x1 = RHit(T + 1), x2 = RLit (T + 1), x3 = RHih(T + 1), x4 = RLih(T + 1),

x5 = RHot(T + 1), x6 = RLot(T + 1), x7 = RHoh(T + 1) andx8 = RLoh(T + 1).


According to the definition of the input variables, we can deduce the Boolean functionsin the core circuit. Firstly, we established the truth table of input states in terms of thestate of temperature–humidity sensors. The truth table of output operations was formulatedto construct psychrometric processes. The Boolean expressions between input and outputvariables for the logical system were deduced and simplified by using the Matlab programdeveloped by the Quien–McCluskey algorithm, whereas an Excel program was also used toverify the correctness of Boolean functions (the detailed derivation may be requested fromthe authors). The simplified Boolean expression of nine input variables and four outputvariable is:

Y1 = x1 · x2 · (x3 + x4) · (x5 + x6) · (x7 + x8), (7)

Y2 = x1 · x2 · x3 · x4 · x5 · x6 · x7 · x8, (8)

Y3 = (x1 + x2) · x3 · x4 · (x5 + x6) · (x7 + x8), (9)

Y4 = x1 · (x7 + x8) · [x4 · x6 · (x9 · x3 + x2) + x2 · x3 · (x5 + x6) + x3 · x4 · x5 · x6]

(10)

We secondly transformed Boolean functions into switching circuits (Fig. 3) and then thetransformation of a PLC program was systematically obtained.

We transformed the equivalent mathematical pattern of forward circuits and Eqs.(5)and(6) into a PLC program (Fig. A.1a in Appendix A). Similarly, the other equations asshown inFig. 3 were also completely transformed into the PLC program. The switchingcircuits of core (Fig. 3) in conjunction with the time-sequence control functions were thenused to protect the operational equipment and to promote the modulating performance. Byusing these equivalent mathematical forms for control switching circuits, we can rapidlyand progressively transform the switching circuits of core (Fig. 3) into a PLC program(Fig. A.1b in Appendix A). The completed PLC program could be implemented to con-trol the temperature–humidity environment of a grafted seedling acclimatization cham-ber (the detail of the transformative procedures and results may be requested from theauthors).

3. Results and discussion

Based on the meteorological information of the Ilan region of Taiwan during 1971–2000(http://www.cwb.gov.tw/v4e/index.htm), the lowest average temperatures occurring in Jan-uary and February were 16.0 and 16.4◦C, respectively, whereas the highest average tem-peratures occurring in July and August were 28.4 and 28.0◦C, respectively. The averagetemperatures in other months were 17.3–26.5◦C. We, therefore, chose the experimentaltime interval in winter, spring and summer, respectively, from January 20 to February 10(temperatures were 10–18◦C), March 20 to April 10 (20–25◦C) and July 20 to August 10(25–38◦C).

http://www.cwb.gov.tw/v4e/index.htm


We interpreted the control results associated with the response variation curves of temper-ature and RH on a daily basis during winter, spring and summer. Moreover, a psychrometricchart of the control target area confined by setting temperatures and RHs was also used toillustrate the controller performance. We compared the grafted seedlings acclimatized un-der the cover in field with acclimating in the chamber, based on the survival rate of graftedseedlings in different seasons and acclimatization environments.

The set points for temperature ranges of free cooling in winter, spring and summer were10–18, 18–26 and 26–34◦C, respectively, whereas the set points for RH ranges of freecooling were 50–80, 70–90 and 80–90%, respectively, in sunny, cloudy and rainy days. Thecontrol target range of the temperature–humidity environment in the chamber was set at26–28◦C and 80–90% in any season.

Fig. 4 illustrates the results when the chamber was expectably controlled at a specificset point ranges of 26–28◦C temperature and 80–90% RH. The time period of illuminationin the chamber was from 19:00 to 07:00. The heat sources produced by the plant-lamps(1800 W) were used to keep the indoor temperature at 27.0–27.9◦C without engaging

Fig. 4. The performance of the temperature–humidity environmental controller in an acclimatization chamber forgrafted seedlings during winter: (a) response variation curves of temperature, (b) a psychrometric chart illustrationof control target area for both temperature and RH and (c) response variation curves of RH.


the heater. The environmental operations of free cooling were intermittently performed todecrease the inner surplus heat, yet to change the indoor RH at 80.1–89.9%. The humidifierswere intermittently operated to increase the indoor RH. The plant-lamps were switched offby a timer after 07:00 h. Since the outdoor temperature was lower than that of indoor inwinter, the indoor RH was usually higher than the upper-limit RH of 90%. The heater wasstarted to reduce the indoor RH until the two-position setting of RH at 85%. When theheater was intermittently used to warm and dehumidify the indoor temperature–humidityenvironment, the chamber was operated by a closed system. The indoor temperature andRH were regulated at 26.8–27.3◦C and 86.2–88.8%, respectively.

The control target of the indoor temperature–humidity environment in spring is shownin Fig. 5. The daily indoor temperature and RH were controlled at 26.2–27.9◦C and84.6–87.9%, respectively. The time period of without illumination in the chamber wasfrom 19:00 to 07:00. Since the plant-lamps (1200 W) were switched off after 19:00 h, theheat in the chamber was not enough to keep the indoor lower-limit temperature at 26◦C.From 17:40 to 21:50, the free cooling was operated to regulate the indoor environment until

Fig. 5. The performance of the temperature–humidity environmental controller in an acclimatization chamber forgrafted seedlings during spring: (a) response variation curves of temperature, (b) a psychrometric chart illustrationof control target area for both temperature and RH and (c) response variation curves of RH.


the indoor temperature was lower than the lower-limit temperature of 26◦C. The heater wasimmediately and intermittently started to warm the indoor temperature until the plant-lamps(1200 W) were started at 07:00 h by a timer. The free cooling was automatically performedto modulate the indoor environment again after 07:00 h.

Fig. 6 illustrates the indoor temperature and RH environments were regulated at27.3–27.6◦C and 83.1–87.2%, respectively, during summer. When the initial temperatureand RH in the chamber were 29.1◦C and 79.5%, the air conditioner associated with thehumidifiers was automatically operated to regulate the indoor temperature and RH until theindoor temperature was lower than the upper-limit temperature of 28◦C. The plant-lamps(1200 W) were switched on after 19:00 h, the free cooling associated with the humidifierswas firstly performed to decrease the indoor surplus heat and to keep the indoor tempera-ture and RH at 27.3–27.6◦C and 83.1–87.2%, respectively. Since the time period of withoutillumination in the chamber was regulated from 07:00 to 19:00 h, if the outdoor temper-ature and RH were suitable for modulating the indoor temperature and RH of the control

Fig. 6. The performance of the temperature–humidity environmental controller in an acclimatization chamberfor grafted seedlings during summer: (a) response variation curves of temperature, (b) a psychrometric chartillustration of control target area for both temperature and RH and (c) response variation curves of RH.


Fig. 7. The survival ratios (%) of grafted seedlings in different seasons and acclimatization environments.

target, the free cooling associated with the humidifiers was firstly engaged. Otherwise, thecontroller would close the vents to form a closed system, and the other suitable operationswere performed in accordance with indoor states and psychrometric processes settings.

The acclimating experiments of the seedlings were, respectively, kept in the chamber andmoved to the field under protected cover after grafting.Fig. 7indicates that the survival rateof grafted seedlings kept in the chamber were 96.2, 97.5 and 97.4% in spring, summer andwinter, respectively. An overall seasonal survival rate was 97.03± 0.64% (mean± S.D.)by using the Boolean algebra-based controlled chamber grafting, that is higher than that of90.17± 5.16% when employing field operations. A higher survival rate is shown for theseedlings acclimated in the chamber after grafting as compared to those grafted seedlingsacclimated under the protected cover in the field, especially in winter (Fig. 7). A majorcomplication in the evaluation of the survival rates for grafted seedling acclimated in thechamber and under the protected cover exists because of the uncertainty from the envi-ronmental management variability (especially in the field) and variance among individualscaused by the grafting procedure.

After acclimating, we can adjust the indoor temperature–humidity environment of thecontrol target to adapt the grafted seedlings to the seasonal changes for increasing thesurvival ratio of the domesticate period. The domesticate period of the grafted seedlingsacclimated in the chamber were reduced from 21 to 14 day during winter comparing withthe conventional culture in the under protected cover in the field.

A dynamic heat balance differential equation in the chamber was obtained to estimateand demonstrate the indoor temperature difference rate caused by the controlled heater dur-ing winter (e.g., dTr/dt= 0.084◦C min−1). Similarly, the indoor temperature and moisturevariation rate caused by air conditioner and humidifiers were also obtained during summerand spring by calculating the equation of mass–energy equilibrium and processing experi-ment, respectively. In this paper, we considered not only the traditional models such as thedifferential or dynamic equations in the form of “input–output” asy=Cx, wherex is input,ythe output andC is presented by some operational mechanisms. We adopted logical modelshaving also a type “input–output,” e.g., the formula∀x(A(x)) ⇒ ∃yB(x, y), whereA andB


are formula-mechanisms of a logical language, that can be interpreted as a statement thatfor every value of the inputx such thatA(x) is valid and the output has the valuey suchthatB(x, y) holds (Vassilyev, 1997). For example, the blocks marked “F-212W(WNDW)”and “F-12W(CMP)” (Fig. A.1a inAppendix A) take the data from the sensors and convertthem into a form which the Boolean logical controller can employ, i.e., the data from a setof temperature and humidity sensors might be converted from measurable and quantifiabledegrees into Boolean logical state variables. The output of the logic controller is actually aset or range of response (e.g., a heater and humidifiers, or only a heater with a proportionalaction). Hence, a system behavior is described through the discrete definition or propertiesof values of variables, e.g., Eqs.(5) and(6)⇒ ∀x(A(x)), whereA is the functions combinedwith the discrete states and two-position actions, and Eqs.(7)–(10)⇒ y(B(x, y)), whereBis the logical mechanisms combined with the Boolean algebra and psychrometric processes.Therefore, input and output are connected indirectly by these properties corresponding toeach other and being described in a logical function.

A logical control system applies a set of control rules suitable for various situations whichmay overlap or confine each other. The final operation of action is a judgment, which issome appropriate combination of all relevant factors. A traditional feedback control systemmakes its decision about what to do based on either a mathematical model of the process or aproportional-integral-derivative (PID) controller (a fixed set of mathematical relationships).In the present research, the logical controller is an implement based on the control paths(e.g., logical rule and operating constrains) coupling with mass–energy equilibrium equa-tions and experiences. It was simpler to solve the complex problems existing in the mixedsystem that includes some classes of discrete event systems, constrained linear systems andnonlinear systems which can be approximated by piecewise linearization than that of theclassical control. In future work, Boolean logical controllers can be used in conjunctionwith traditional PID controllers or fuzzy logic controllers more precisely and completely toaccount for the real systems.

4. Conclusions

Our work demonstrates that automatic networks (switching circuits) linked and formu-lated by both Boolean functions and psychrometric processes are the important componentsof the environmental controller for a grafting seedling acclimatization chamber. It is veryuseful and suitable for use in proposing some qualitative method of their control targetinstead of exhaustive numerical methodology under all admissible initial states, parame-ters, and disturbances. The mathematical models described by logical variables were easilyimplemented to control on-line by a PLC or a graphic control program (e.g., LabVIEW) ina PC. The methodology could overcome the difficulties of accidentally occurring divergentproblems caused by choosing initial state-variable vectors.

Using the methodology and technique, we implemented the environmental controllerfor grafted seedlings in the acclimatization chamber. The controller performances demon-strate that the methodology is realizable and the control system can satisfactorily achieveexpected goals for providing suitable curing conditions and modulating the environmentalfactors such as temperature, RH, illumination and CO2 for grafted seedlings in the acclima-


tization chamber. The acclimating experiments of the grafted seedlings resulted in an overallseasonal survival rate of 97.03± 0.64% by using Boolean algebra-based chamber grafting,which was higher than that of 90.17± 5.16% by employing field operations.

Acknowledgements

This work was supported by the National Science Council of Republic of China underGrant NSC91-2313-B197-007. Sincere thanks go to seedlings farm owners for providingvaluable information and for use of their seedlings farms, without which this research workwould have not been possible. We also thank Dr. Suming Chen, editor Dr. Sidney Cox andtwo anonymous reviewers for providing constructive comments in the manuscript.

Appendix A

Fig. A.1.

Fig. A.1. (a) The equivalent mathematical pattern of forward circuits as well as Eqs.(5) and(6) were transformedinto a PLC program and (b) a PLC program was developed by transforming and compiling the switching circuitsof core.


Fig. A.1. (Continued).

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